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Theorem con34b 285
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )

Proof of Theorem con34b
StepHypRef Expression
1 con3 128 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
2 ax-3 9 . 2  |-  ( ( -.  ps  ->  -.  ph )  ->  ( ph  ->  ps ) )
31, 2impbii 182 1  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178
This theorem is referenced by:  mtt  331  pm4.14  563  dfom2  4657  weniso  5813  dfsup2  7190  wemapso2lem  7260  pwfseqlem3  8277  indstr  10282  rpnnen2  12498  algcvgblem  12741  isirred2  15477  isdomn2  16034  ist0-3  17067  mdegleb  19444  dchrelbas4  20476  ltl4ev  24390  supnuf  25028  supexr  25030  raldifsni  26152  isdomn3  26922  conss34  27044
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179
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